Four-Note Chords in Four Voices

Tom Johnson

How can we classify musical harmonies? Terms like “major seventh” and “diminished ninth” can mean quite a few different things, and it was not until 1973 that this little problem of musical taxonomy was solved definitively and elegantly in Allen Forte’s book The Structure of Atonal Music. More recently Guerino Mazzola, Elliot Carter and other writers have counted and classified harmonies somewhat differently, but the Forte classifications have become the standard. Theorists today who wish to identify clearly a certain type of chord will not use terms like “minor seventh,” but will distinguish between Forte 4-19 and Forte 4-26.

As a composer I often think about what kinds of harmonies go together and how to place them in groups, and this problem is particularly apparent in the case of four-note chords, because we use them so much and hear them so well. There are 495 ways to distribute 12 notes in groups of four, and thanks to Forte, we now know that they break down into exactly 29 sets. The goal of this composition is to allow listeners to better appreciate the pure harmonic richness of all these combinations of notes and to help them hear the differences between one set and another. Wanting to place the emphasis on harmony itself, without rhythms and colors, I wrote the music simply in half notes in four lines, playable either on keyboard or by a string quartet, but also by other ensembles.

At first it seemed that the piece must have 29 short movements, following Forte’s 29 sets, but this way the music was starting and stopping all the time, and besides, sets like Forte 4-2 and Forte 4-3 sound very similar, because they have the same “bip”. Bip is another Forte term meaning “basic interval pattern,” and in this case the bip is 112, meaning that if you place the four notes as close together as possible, the distance between adjacent notes will be some ordering of 1, 1, and 2 semitones.

The piece is dedicated to Forte, not only in recognition of his important theoretical work, but also because I learned so much from him as a young naïve Yale student in 1959-61.


Four-Note Chords in Four Voices

  • Tom Johnson
  • Year of composition: 2009
  • Instrumentation: string quartet


On disc